To see how this works, consider again the single tripartite tensor example.
The canonical purification \(\mathinner {|{\sqrt{\rho _{AB}}}\rangle }_{A A^\star B B^\star }\)  following this procedure corresponds to a tensor network with two tensors \(T_{ABC}\)  and \(T^*_{ABC}\)  contracted along leg \(C\) .
This however is not exactly the analog of gluing two copies of the entanglement wedge together. The difference is that these two tensors are now correlated. Normal tensor network analogs of any given geometry discretize that geometry with a collection of tensors that are all chosen independently at random. Hence the random tensor network analogous to the glued entanglement wedges from gravity [1]} would have completely uncorrelated tensors in the two copies!
